US5424948A - Locomotive traction control system using fuzzy logic - Google Patents
Locomotive traction control system using fuzzy logic Download PDFInfo
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- US5424948A US5424948A US08/150,645 US15064593A US5424948A US 5424948 A US5424948 A US 5424948A US 15064593 A US15064593 A US 15064593A US 5424948 A US5424948 A US 5424948A
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B60—VEHICLES IN GENERAL
- B60T—VEHICLE BRAKE CONTROL SYSTEMS OR PARTS THEREOF; BRAKE CONTROL SYSTEMS OR PARTS THEREOF, IN GENERAL; ARRANGEMENT OF BRAKING ELEMENTS ON VEHICLES IN GENERAL; PORTABLE DEVICES FOR PREVENTING UNWANTED MOVEMENT OF VEHICLES; VEHICLE MODIFICATIONS TO FACILITATE COOLING OF BRAKES
- B60T8/00—Arrangements for adjusting wheel-braking force to meet varying vehicular or ground-surface conditions, e.g. limiting or varying distribution of braking force
- B60T8/17—Using electrical or electronic regulation means to control braking
- B60T8/1701—Braking or traction control means specially adapted for particular types of vehicles
- B60T8/1705—Braking or traction control means specially adapted for particular types of vehicles for rail vehicles
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B60—VEHICLES IN GENERAL
- B60T—VEHICLE BRAKE CONTROL SYSTEMS OR PARTS THEREOF; BRAKE CONTROL SYSTEMS OR PARTS THEREOF, IN GENERAL; ARRANGEMENT OF BRAKING ELEMENTS ON VEHICLES IN GENERAL; PORTABLE DEVICES FOR PREVENTING UNWANTED MOVEMENT OF VEHICLES; VEHICLE MODIFICATIONS TO FACILITATE COOLING OF BRAKES
- B60T8/00—Arrangements for adjusting wheel-braking force to meet varying vehicular or ground-surface conditions, e.g. limiting or varying distribution of braking force
- B60T8/17—Using electrical or electronic regulation means to control braking
- B60T8/174—Using electrical or electronic regulation means to control braking characterised by using special control logic, e.g. fuzzy logic, neural computing
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- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y10—TECHNICAL SUBJECTS COVERED BY FORMER USPC
- Y10S—TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y10S706/00—Data processing: artificial intelligence
- Y10S706/90—Fuzzy logic
Definitions
- This invention relates generally to a traction control system and, more particularly, to a traction control system using fuzzy logic to control wheel slip of the drive wheels of a train locomotive in order to maximize the coefficient of friction between the drive wheels and the rail interface.
- train locomotives such as diesel electric locomotives, used to move railway cars along a dual rail configuration are propelled by exerting torque to drive wheels associated with the locomotive that are in contact with the rails.
- the power to propel the locomotive is first developed as mechanical energy by a high horsepower diesel engine.
- the diesel engine drives a generator that converts the mechanical energy to electrical energy.
- the electrical energy is then converted back to mechanical energy by a series of traction motors.
- One traction motor is rigidly connected to each axle associated with a pair of drive wheels such that when the axle is rotated, the drive wheels also rotate. In this manner, each traction motor is in parallel with the generator and rotates independently of the other axles.
- the specifics of the mechanisms for propelling a locomotive are well known.
- Friction between the drive wheel and the rail interface provides the traction for causing the movement of the locomotive. If there were no friction between the drive wheels and the rail surface, the wheels would rotate and slip relative to the rails without providing movement to the locomotive.
- the friction force is a function of the coefficient of friction between the drive wheels and the rail interface, and the downward force exerted by the locomotive on the rail.
- Wheel slip is the value that characterizes the difference in linear speed between the locomotive and the drive wheels. The more friction between the drive wheels and the rail surface, the more traction can be generated, and thus, the more propelling force is available to move the locomotive. It is possible to increase the friction force between the drive wheels and the rail surface by increasing the weight of the locomotive. However, certain well understood engineering and economic factors make this option unattractive. Therefore, locomotives incorporate traction control systems in order to maximize the friction force between the drive wheels and the rail surface, so as to maximize the propelling force of the traction motors.
- a traction control system may have two control variables that can be used to control the amount of wheel slip of the drive wheels relative to the rails.
- the power output of the generator can be reduced, which leads to lower traction motor torques, which in turn leads to less force causing the drive wheels to spin.
- reduced generator power provides less power to propel the locomotive.
- the locomotive can drop sand in front of the wheels, thus creating a greater friction relationship between the drive wheels and the rail surface.
- limited payload and cost of sand require that this method of control be used conservatively. Consequently, the only practical way to maximize the friction force is to maximize the value of the coefficient of friction between the drive wheels and the rails.
- FIG. 1 shows a graphical relationship between the coefficient of friction on the vertical axis and the percent of wheel slip on the horizontal axis for dry, wet and oily rail conditions.
- a graph line for each coefficient of friction versus percentage of wheel slip is given for the different rail conditions in each direction of rotation of the drive wheels.
- the coefficient of friction is at its maximum at about 10% wheel slip. It is noted that under ideal dry rail conditions, the torque that a locomotive engine can generate is not high enough to cause the wheel slip to increase to this value. Once the rail becomes wet and/or oily, the percentage of wheel slip at which the maximum coefficient of friction is attained increases. Particularly, for a wet rail condition, the maximum coefficient of friction is at approximately 15% wheel slip.
- each graph line before reaching the peak is a stable region of operation, however, the region of each graph line beyond the peak is an unstable region in which predictable wheel rotation is indeterminable.
- the goal, therefore, of a traction control system that attempts to maximize the coefficient of friction is to operate as close to the peak of the friction/slip curve as possible, while avoiding the unstable region.
- the general strategy of the traction control system is to estimate the slip level at which the friction/slip curve reaches its peak value, and to regulate the system so that the wheel slip does not exceed this value.
- control action must be taken to remain in the stable region. This task is made more difficult because the exact characteristics of the friction/slip curve is never known as rail conditions can rapidly change causing the estimated peak to be at a higher slip value than the actual peak. Abnormal rail conditions may cause a friction/slip characteristic that increases asymptotically to a maximum coefficient of friction.
- a traction control system must limit wheel oscillation while correcting the estimation of the friction/slip curve peak.
- Prior art traction control systems generally consist of cascaded single input and single output controllers.
- the innermost controller loop controls the generator's field current by varying the generator's field voltage source.
- a reference field current is generated by a generator output controller for establishing the generator field current.
- the generator output controller regulates the generator so the generator's operating characteristics follow a desired pattern based on a system model of the locomotive.
- the system model would include a generator model, a generator field model, and a model representing the field current controller and the generator output controller.
- a simplification can be made because the closed loop response of the actual generator controller is known.
- Traction control system models which define the rotation of an axle generally assume that the wheels associated with an axle rotate at the same angular velocity and experience the same coefficient of friction. In reality, differences in the coefficient of friction exist between the two wheels of an axle exists such that torsional forces are generated in the wheel axle and differing angular velocities occur for the two wheels.
- a locomotive traction control system which incorporates the use of fuzzy logic to maximize the coefficient of friction between the locomotive drive wheels and the rails on which the wheels ride.
- the locomotive traction control system includes a fuzzy logic slip controller that provides a generator current reference signal to a generator controller controlling the field current of a generator associated with the locomotive.
- the generator generates electricity which energizes electrical traction motors for driving the drive wheels.
- the fuzzy slip controller determines the appropriate generator current reference signal that will cause the generator controller to provide an output of the generator to cause a predetermined wheel slip regardless of the rail condition.
- a fuzzy logic slip reference estimator uses the same variables as the fuzzy slip controller to generate a wheel slip reference signal indicative of the desirable wheel slip depending on the current rail conditions that will maximize the coefficient of friction.
- the slip reference signal is applied to the fuzzy slip controller so as to update the generator current reference signal to be consistent with the maximum coefficient of friction for that rail condition. Therefore, the fuzzy slip controller will provide a signal to the generator control so as to control the generator of the locomotive to output the appropriate power for the maximum coefficient of friction.
- FIG. 1 is a graph showing the relationship between percent of wheel slip on the horizontal axis and the coefficient of friction on the vertical axis between drive wheels of a locomotive and the rail surface;
- FIG. 2 is a block diagram of a locomotive traction control system according to a preferred embodiment of the present invention
- FIG. 3 is a block diagram of the fuzzy logic slip controller of the locomotive traction control system of FIG. 1;
- FIGS. 4-6 are graphs of the membership function sets for change in wheel slip, stability and wheel slip error, respectfully;
- FIG. 7 is a graph of the membership function set for a defuzzification step of the fuzzy logic slip controller of FIG. 3;
- FIG. 8 is a more detailed graph showing the relationship between the percent of wheel slip for the slip reference on the horizontal axis and the coefficient of friction on the vertical axis.
- the traction control system 10 includes a generator controller 12, a field current controller 14 and plant dynamics 16.
- the generator controller 12 receives generator voltage, generator current and power limit control signals as inputs from other locomotive control systems, such as an operator controller.
- the generator controller 12 provides a field current reference signal to the field current controller 14.
- the field current controller 14 outputs a field voltage signal to the plant dynamics 16.
- the plant dynamics 16 is representative of at least the engine, the generator and the traction motors of the locomotive.
- the field current reference signal adjusts the field current of the generator so as to modify the power output of the generator. This, in turn, will effect the torque applied to the drive wheels of the locomotive.
- a feedback signal of the field current is sent from the plant dynamics 16 to the field current controller 14. Additionally, a feedback signal of the generator voltage and current is sent from the plant dynamics 16 to the generator controller 12. As will be discussed in detail below, the generator controller 12 also receives an input signal from a fuzzy logic slip controller 18 such that the generator controller 12 uses all of the above mentioned input signals to determine the appropriate field current reference signal.
- the specific components and operation of the generator controller 12, the field current controller 14 and the plant dynamics 16 are common in typical locomotives, and are well known to one skilled in the art.
- wheel slip ( ⁇ ) can be controlled by changing the torque of the traction motors driving the drive wheels. Further, the torque generated by a series wound DC motor, as are the traction motors, is approximately proportional to the motor current. Hence, by adjusting the motor current, the wheel slip ⁇ can be controlled.
- the fuzzy slip controller 18 provides a generator current reference signal to the generator controller 12 so as to cause the generator controller 12 to adjust the generator output to change the wheel torque, and thus, control the wheel slip ⁇ .
- the fuzzy logic slip controller 18 will set the motor current to provide a predetermined reference wheel slip ⁇ , for example 5% wheel slip, regardless of the rail condition.
- the fuzzy slip controller 18 receives drive wheel speed, ground speed and motor current signals from the plant dynamics 16 in order to determine the appropriate generator current reference signal for the desirable wheel slip ⁇ .
- the fuzzy slip controller 18 receives a slip reference ( ⁇ reference ) signal from a fuzzy logic slip reference estimator 20.
- the fuzzy logic slip reference estimator 20 also receives the wheel speed, ground speed and motor current signals from the plant dynamics 16 in order to determine the rail conditions so as to generate the slip reference ⁇ reference signal that will cause the fuzzy slip controller 18 to adjust the generator current reference signal to provide the appropriate slip for a maximum coefficient of friction.
- the architecture of the fuzzy slip controller 18 and the fuzzy slip reference estimator 20 is common to many types of fuzzy logic controllers known in the art such as a proportional integral (PI) controller. For a detailed discussion of fuzzy logic controllers, one can see C.
- PI proportional integral
- FIG. 3 a detailed block diagram of the fuzzy slip controller 18 is shown.
- all of the traction motors of the locomotive are connected in parallel to the generator. This configuration requires that only one of the motor currents is controllable at any given time.
- the traction motor for which the current is being controlled is referred to as the target motor. Since having a wheel speed above the wheel slip reference ⁇ reference is more serious than a wheel speed below the wheel slip reference ⁇ reference due to the fact that it is undesirable to operate in the unstable region of the friction/slip relationship, the wheel with the largest amount of slip is designated the target motor. Therefore, the wheel speeds for all of the drive wheels are applied to a system 22 which selects the drive wheel with the fastest spin.
- a system 24 is incorporated for determining and normalizing delta calculations.
- the wheel speed of the fastest wheel from the system 22, each of the traction motor currents and the slip reference ⁇ reference signal from the slip reference estimator 20 are applied as inputs to the system 24.
- the system 24 determines a raw wheel slip error ( ⁇ error ) as the difference between the actual wheel slip ⁇ and the slip reference ⁇ reference , a raw change in motor current ( ⁇ I motor ) between subsequent sampling times, and a raw change in wheel slip ⁇ between the current wheel slip ⁇ and the wheel slip at a previous sample time.
- ⁇ error a raw wheel slip error
- k represents a present sample time and k-1 represents a previous sample time.
- K 1 , K 2 and K 3 are predetermined normalization scaling factors or gain constants selected depending on the system models of the particular locomotive.
- the motor current I motor is proportional to motor torque. If the friction/slip relationship is in the stable region, the wheel slip ⁇ rate of change and the motor current I motor rate of change will have the same sign. If the friction/slip relationship is near the peak, a large change in the wheel slip A will result in a proportionally smaller change in the motor current I motor . If the unstable region is entered, the rate of change of the wheel slip ⁇ and the motor current I motor will have opposite signs. Therefore, it is necessary to determine which of the three regions of peak, stable or unstable the system is operating.
- a measure of stability (a) is calculated as follows:
- the raw ⁇ is then normalized for fuzzification as follows: ##EQU2##
- the stability ⁇ will be negative when the wheel slip ⁇ and the motor current I motor are changing in opposite directions, positive when these values are changing at different rates but in the same direction, and zero when these values are changing at the same rate.
- the normalized wheel slip error ⁇ error , change in wheel slip ⁇ and the stability ⁇ are next fuzzified by a fuzzification system 26.
- Each of ⁇ , ⁇ error and ⁇ are represented by a membership function set for fuzzification.
- a membership function is a real number classification of a linguistic description. In other words, a real number value is defined for each descriptive change in wheel slip ⁇ , the slip error ⁇ error and the stability ⁇ .
- the use of membership functions to define a description is well understood in fuzzy logic applications.
- FIGS. 4-6 show membership function sets for each of the change in the wheel slip ⁇ , the stability ⁇ , and the slip error ⁇ error , respectfully. Membership function values are given on the vertical axis and the normalized values for ⁇ , ⁇ , or ⁇ error are given on the horizontal axis.
- the membership function set for ⁇ is selected to be negative, zero, and positive, as shown in FIG. 4.
- a small membership function set is chosen because the ⁇ calculations are susceptible to system noise and higher order system characteristics. For this reason, the membership function set for ⁇ provides a significant overlap between each of the members in the set. A small amount of overlapping between the membership functions causes undesirable abrupt changes in the output of the controller 18.
- the zero membership function is defined as the area beneath a triangle which begins at the -1.0 location on the ⁇ axis, reaches a peak at the 1.0 membership function value above 0.0 ⁇ , and descends to the 1.0 location on the ⁇ axis.
- the negative membership function is defined as the area beneath a line that extends from the 1.0 membership function value to approximately the 0.0 location on the ⁇ axis.
- the positive membership function is defined as the area beneath a line that extends positively approximately from the 0.0 location on the ⁇ axis upward to the 1.0 membership function value.
- the normalized ⁇ value is first determined from equations (3) and (5), and is located on the horizontal axis in FIG. 4.
- a vertical line is extended upward from this location to determine an intersection between this line and the membership function lines.
- By extending a horizontal line from the intersection between the vertical line and the membership function lines to the vertical axis establishes the membership function values for the particular ⁇ value.
- the ⁇ value calculated from equation (5) was found to be -0.25.
- an intersection with the negative membership function line occurs at approximately 0.25
- an intersection with the zero membership function line occurs at approximately 0.75. Therefore, these are the membership function values for this particular change in wheel slip ⁇ .
- the membership function set for stability ⁇ is the same as the membership function set for the change in wheel slip ⁇ except that the membership functions are labeled unstable, stable and peak instead of negative, zero and positive, respectfully, as shown in FIG. 5.
- the stability ⁇ is determined by equations (7) and (8), and the appropriate membership function values are determined from this stability value in FIG. 5 in the same manner as discussed above for the ⁇ membership function values.
- the membership function set for the slip error ⁇ error consists of seven membership functions, as shown in FIG. 6.
- Each of the seven membership functions is labeled as one of negative big (NB), negative medium (NM), negative small (NS), zero even (ZE), positive small (PS), positive medium (PM), and positive big (PB).
- NB negative big
- NM negative medium
- NS negative small
- ZE zero even
- PS positive small
- PM positive medium
- PB positive big
- the value for NB is a relatively big negative number
- the value for NM is a relatively medium negative number
- the value for NS is a relatively small negative number
- the value for ZE is exactly zero
- the value for PS is a relatively small positive number
- the value for PM is a relatively medium positive number
- PB is a relatively large positive number.
- the quality of the error signal is sufficient to support the seven membership functions.
- the NB membership function is defined as the area beneath the line which starts at the 1.0 membership function value and intersects the ⁇ error axis at approximately -0.7.
- the NM membership function is defined as the area beneath the triangle which starts as the -1.0 ⁇ error value, reaches a peak at approximately the -0.7 ⁇ error value, and descends to approximately the ⁇ error -0.3 value.
- the NS membership function is defined as the area beneath the triangle that starts at the -0.7 ⁇ error value, reaches a peak at approximately the -0.5 ⁇ error value, and descends to approximately the 0.0 ⁇ error value.
- the ZE membership function is defined as the area beneath the triangle that starts at the -0.5 ⁇ error value, reaches a peak at approximately the 0.0 ⁇ error value and descends to approximately the 0.3 ⁇ error value.
- the PS membership function is defined as the area beneath the triangle that starts at the 0.0 ⁇ error value, reaches a peak at approximately the 0.3 ⁇ error value and descends to the 0.7 ⁇ error value.
- the PM membership function is defined as the area beneath the triangle that starts at the 0.3 ⁇ error value, reaches a peak at the 0.7 ⁇ error value and descends to the 1.0 ⁇ error value.
- the PB membership function set is defined as a line that extends from the 0.7 ⁇ error value to the 1.0 membership function value.
- the fuzzified slip error ⁇ error and the fuzzified delta slip ⁇ could be used as the inputs to a standard fuzzy PI knowledge base to a formslip controller.
- the design objective is to create a controller that is robust enough to handle the control of the system when it is operating in the unstable region of the friction/slip relationship.
- the addition of the change in the target motor current ⁇ I motor allows the measure of stability ⁇ to be calculated which provides additional information that can be incorporated into the knowledge base 30.
- the additional stability information can be used to provide the desirable robustness.
- the slip controller 18 can be thought of as a meta-controller with three low-level controllers. Particularly, one low-level controller is assigned for each region of the friction/slip relationship designated as the peak, stable and unstable regions. Each low-level controller would then produce an output and the three outputs would be combined by the meta-controller depending on the measure of stability.
- Table I shows how the appropriate outputs are determined depending on the region of operation. In Table I, outputs are selected by taking the appropriate change in wheel slip ⁇ as positive, zero or negative, and the slip error ⁇ error as one of the seven membership functions PB, PM, PS, ZE, NS, NM and NB for each region of stability.
- the modified PI controller knowledge base is shown in the first section of Table I labeled as " ⁇ is Peak".
- the standard PI controller knowledge base is shown as the second section of Table I labeled as " ⁇ is Stable”.
- the unstable meta-controller knowledge base 30 is used as given by:
- the knowledge base 30 of Table I consists of rules numbered from 1 to 63, where each rule has three predicates. Each rule is labeled according to the notation of the membership function set of FIG. 6. Two additional rules are defined as positive zero (PZ) and negative zero (NZ) having values slightly more and slightly less than zero, respectively.
- the inference engine 28 determines and outputs the degree of applicability ( ⁇ ) for each of the 63 rules.
- the degree of applicability ⁇ is defined as the minimum membership function value for each rule of Table I.
- ⁇ output values for each rule of Table I are applied to a defuzzification system 32.
- a height defuzzification method is used by this system.
- the height method of defuzzification is a well known procedure that determines a weighted average of an output membership function's center of gravity.
- a weighting function for each rule is its corresponding degree of applicability ⁇ .
- a normalized output, ⁇ , of the defuzzification system 32 using the height method is determined by: ##EQU3##
- C i is the midpoint value for each rule that has been fired as determined by an output membership function set consisting of nine equally spaced and symmetric membership functions shown in FIG. 7. These membership functions include NB, NM, NS, NZ, ZE, PZ, PS, PM and PB, mentioned above, arranged in symmetrical triangles as shown.
- the value m is 63 for each of the rules of Table I.
- a standard fuzzy PI uses seven different outputs. The two additional membership functions (PZ, NZ) were added so that exaggerated control actions could be taken under the special conditions discussed earlier in the unstable region.
- the symmetric quality of each output membership function causes its center of gravity to be unchanged as it is clipped or scaled. The constant center of gravity simplifies the defuzzification process.
- Rule 20 is NS
- Rule 21 is ZE
- Rule 23 is NZ
- Rule 24 is PZ
- Rule 29 is NZ
- Rule 30 is PZ
- Rule 32 is ZE
- Rule 33 is PS.
- the output of the defuzzification system 32, ⁇ u, is scaled and integrated to determine the generator current reference signal (I gr ), as depicted by a scale, integrate and bound system 34.
- the generator current reference signal I gr is given as:
- K 4 is a gain constant and I gr-1 is a generator current reference signal from the previous sample time.
- the generator may not be able to develop the amount of current desired.
- the integrator for the generator current reference signal should be adjusted under these special conditions.
- the generator current reference signal When the generator current reference signal is above the maximum generator current, the generator current reference signal should be limited to the maximum generator current.
- the slip controller 18 When the generator is operating at its voltage or power limit, the slip controller 18 is ignored and becomes an open loop. When this occurs, the generator current reference signal should be set to the actual generator current being measured.
- the ideal sampling time of the slip controller 18 is 20 ms because existing generator controllers operate at a cycle time of this value. If the slip controller 18 were to operate at a faster rate than the generator controller 12, this would result in useless intermediate calculations by the slip controller 18. The slip controller 18 could be operated at a slower rate resulting in an inferior transient response.
- the choice of a sampling rate for a fuzzy logic controller is subject to the same considerations that determine the sampling rate for a standard discrete controller.
- the performance characteristics of the slip controller 18 can be adjusted by changing the normalization gain constants K 1 , K 2 , K 3 and K 4 .
- the slip error ⁇ error normalization gain constant factor K 1 of equation (4) should be set so that zero slip always corresponds to a normalized slip error of -1.0. Therefore, the slip error normalization gain constant K 1 is defined as: ##EQU4## Adjusting the slip error normalization gain constant K 1 as the slip reference ⁇ reference changes deemphasizes the slip error ⁇ error as the slip reference ⁇ reference increases. This in turn causes the slip controller 18 to become less aggressive at approaching zero slip error ⁇ error as the slip reference ⁇ reference increases. It is desirable to approach high levels of slip more cautiously because the consequences of exceeding the peak of the friction/slip relationship becomes more severe at higher levels of wheel slip ⁇ .
- the change in the wheel slip ⁇ normalization gain constant K 2 of equation (5) is set so that the wheel slip ⁇ is very small when the system is near steady state, and is ⁇ 1.0 during uncontrolled wheel slips.
- the change in the motor current normalization gain constant K 3 of equation (6) is then set so that ⁇ is approximately equal to ⁇ I motor when the system is well within the stable region of the friction/slip relationship. If these two gain controls were not set in this way, the logic of the knowledge base 30 would become less effective.
- the output gain constant K 4 of equation (10) is set by balancing several factors. Because the output of the slip controller 18 is the input to the generator controller 12, the slip controller 18 output should not contain frequencies outside the bandwidth of the generator controller 12. Too large of a gain constant could cause this condition to exist. A large gain constant could also cause excessive control action to occur in response to steady state noise. On the other hand, if the gain constant is too low, the control action will not be sufficient to adequately control the slip. Based on these factors, a middle ground for the output gain constant K 4 is desirable.
- the slip controller 18 is designed to minimize the effects of slip reference signals that are in the unstable region of the friction/slip relationship.
- the slip controller 18 attenuates the oscillations that would normally occur in the unstable region.
- the slip controller 18 does not prevent entry into the unstable region, but does recognize entry into this region and uses appropriate control actions to mitigate the otherwise unfavorable response.
- the slip reference estimator 20 determines the operating region just as the slip controller 18 does. By using the measure of stability ⁇ , the slip error ⁇ error and the change in wheel slip ⁇ , the slip reference estimator 20 determines how the slip reference ⁇ reference should be changed to maximize the coefficient of friction.
- the slip reference estimator 20 uses the same variables, gain constants and membership functions as discussed above for the slip controller 18. Specifically, the values of ⁇ error , I motor , ⁇ , and ⁇ as well as the gain constants K 1 -K 4 , are identical for the slip reference estimator 20 as they were for the slip controller 18.
- the slip reference estimator 20 will incorporate a normalization system, a fuzzification system, an inference engine, a defuzzification system, and a scaling system that are the same as above for the slip controller 18. However, the knowledge base that the slip reference estimator 20 uses is different than the knowledge base of the controller 18.
- slip reference estimator 20 Because the process of determining the slip reference ⁇ reference by the slip reference estimator 20 is the same as the process of determining the generator current reference signal by the slip controller 18, except for the use of a different knowledge base, a detailed block diagram of the slip reference estimator would be the same as FIG. 3, and thus, a block diagram of the slip reference estimator 20 is not shown.
- the discussion below of the slip reference estimator 20 will go directly to the knowledge base.
- the slip reference estimator 20 can be thought of as a meta-estimator with three low-level estimators, just as with the controller 18.
- the meta-estimator knowledge base for the slip reference estimator 20 is given in Table II below. Table II also includes 63 rules, each rule having three predicates.
- FIG. 8 shows a more detailed graphical depiction of the percent wheel slip and the coefficient of friction setting out the stable, peak and unstable regions.
- the controller 18 will attempt to drive the system to steady state, thus reducing the wheel slip error ⁇ error . If the system is operating near the peak region as the slip error ⁇ error is being reduced, the system will become more stable by traversing deeper into the stable region. Under these conditions, the system is not in danger of becoming unstable and the slip reference ⁇ reference does not require lowering. An increase in the slip reference ⁇ reference might be possible, but that adjustment should be made by the stable estimator knowledge base (discussed below) after the system has transitioned.
- the controller 18 When the system is operating in the peak region and the slip error ⁇ error is negative, the controller 18 will continue increasing the slip ⁇ in order to reach the stable region of operation. Increasing the slip ⁇ when the system is already operating in the peak region, would likely cause the unstable region to be entered. In order to avoid this situation, the wheel slip reference ⁇ reference is adjusted downward according to the magnitude of the wheel slip error ⁇ error . The more negative the error is, the more the slip reference ⁇ reference is reduced. If the stability ⁇ is determined to have a membership function for the peak region of the friction/slip relationship, the peak region meta-estimator knowledge base is used as given by:
- the wheel slip ⁇ When the system is operating in the stable region, the wheel slip ⁇ is less than the optimum wheel slip ⁇ *. However, just because the wheel slip ⁇ is in the stable region does not necessarily mean that the wheel slip reference ⁇ reference is in the stable region. Further, if the slip error ⁇ error is positive, then the slip reference ⁇ reference should be in the stable region. Under these conditions, the slip reference ⁇ reference could be raised because the system is operating in the stable region at a level of slip greater than the present slip reference ⁇ reference . Upward adjustment of the slip reference ⁇ reference should only be made when the system is close to steady state. This additional restriction is conservative, but if an upward revision is warranted, it will remain as the system nears steady state.
- the wheel slip reference ⁇ reference should never be increased if the slip error ⁇ error is negative.
- the slip error membership function "ZE" is non-zero for small and negative slip errors. Therefore, the wheel slip reference ⁇ reference should not be increased when the slip error is "ZE" but should be increased when the slip error is truly positive (PS, PM, PB).
- PS power, PM, PB
- Rules (8) and (11) of Table II will fire. If the slip error ⁇ error is very close to zero, Rule (11) will dominate, and the slip reference ⁇ reference will increase slightly. In order to cause a larger increase in the slip reference ⁇ reference under this condition, the output of Rule (8) is PS.
- ⁇ is stable, then use the stable region estimator knowledge base to determine the estimators change in output.
- the stable region estimator knowledge base is shown in the second section of Table II labeled as " ⁇ is Stable”.
- the slip controller 18 can prevent large oscillations from occurring while the system is in the unstable region, operating in the unstable region causes some oscillation.
- the speed of the slip reference ⁇ reference reduction depends on the wheel slip error ⁇ error . Operation in the unstable region while the slip ⁇ is below the reference means the slip reference ⁇ reference is much too high and should be reduced quickly. If the slip is close to or above the slip reference ⁇ reference , the slip reference ⁇ reference should be adjusted downward more slowly. If the stability ⁇ is determined to have a membership function for the unstable region of the friction/slip relationship, the unstable region meta-estimator knowledge base is given by:
- ⁇ is unstable, then use an unstable region estimator knowledge base to determine the controller output.
- the unstable region estimator knowledge base is shown in the third section of Table II labeled as " ⁇ is Unstable”.
- the output of the slip reference estimator inference engine is a fuzzy set representing the change to the slip reference ⁇ reference that should be made.
- the fuzzy output is defuzzified using the height method as discussed above for the output of the slip controller 18 in order to arrive at the ⁇ reference value.
- the friction/slip relationship never reaches a peak and therefore does not have an unstable region.
- high levels of wheel slip ⁇ may theoretically provide more traction, but wear on the rail and wheels become excessive.
- the wheel slip reference ⁇ reference should be limited so that it does not exceed 25% wheel slip. This limit is primarily based on economic factors and is therefore subject to modifications.
- the wheel slip reference ⁇ reference is also subjected to a lower limit. The lower limit is primarily a factor of the accuracy of the actual sensors utilized by the system. Very small levels of slip are subject to calculation errors because the difference between the locomotive velocity and the wheel velocity is very small.
- the initial value for the lower limit of the slip reference ⁇ reference should be set at 2% wheel slip.
- the output of the defuzzification system, A reference is scaled and integrated to determine the new wheel slip reference ⁇ reference defined as follows: ##EQU5## where K 5 is a predetermined gain constant.
- the slip reference estimator's knowledge base is derived based on the same membership functions and normalization factors as the slip controller 18. This is done to simplify the overall system and provide for a more concrete tuning procedure.
- the slip controller 18 should be tuned with the estimator 20 deactivated and a constant slip reference ⁇ reference used in its place. After satisfactory performance of the slip controller 18 is obtained, the slip estimator 20 can be activated. If K 5 is set too large, the estimator 20 will make large corrections when relative little can be inferred about the status of the system. Large changes in the slip reference ⁇ reference will induce undesirable oscillations in the output of the system. A low gain constant K 5 will cause the estimator 20 to lag the system and to track the peak of the friction/slip relationship.
- the above-described fuzzy logic process to determine the appropriate wheel slip for maximum traction can be implemented in many ways. Specifically, it is possible to provide hardware control which performs the desired fuzzification and defuzzification steps. Additionally, it is possible to incorporate the fuzzification and defuzzification steps of the fuzzy slip controller 18 and the fuzzy slip reference estimator 20 as software steps. A specific software implementation of the above described process is shown in the paper by L. Jordan, Jr. referenced above and attached hereto as Appendix A.
Abstract
Description
raw λ.sub.error =λ-λ.sub.reference (1)
raw ΔI.sub.motor =I.sub.motor (k)-I.sub.motor (k-1) (2)
raw Δλλ(k)-λ(k-1) (3)
rawσ=|ΔI.sub.motor -Δλ|[sign(ΔI.sub.motor Δλ)](7)
TABLE I __________________________________________________________________________ Δλ σ is PEAK σ is STABLE σ is UNSTABLE λ.sub.error Positive Zero Negative Positive Zero Negative Positive Zero Negative __________________________________________________________________________ PB NB (1) NB (2) NS (3) NM (4) NM (5) NZ (6) NB (7) NM (8) NM (9) PM NB (10) NM (11) NZ (12) NM (13) NS (14) ZE (15) NB (16) NM (17) NM (18) PS NB (19) NS (20) ZE (21) NM (22) NZ (23) PZ (24) NB (25) NM (26) NM (27) ZE NM (28) NZ (29) PZ (30) NS (31) ZE (32) PS (33) NB (34) NM (35) NM (36) NS NS (37) ZE (38) PS (39) NZ (40) PZ (41) PM (42) NM (43) NM (44) NS (45) NM NZ (46) PZ (47) PS (48) ZE (49) PS (50) PM (51) NM (52) NM (53) NS (54) NB ZE (55) PS (56) PS (57) PZ (58) PM (59) PM (60) NS (61) NS (62) NS (63) __________________________________________________________________________
I.sub.gr =I.sub.gr-1 +ΔμK.sub.4 (10)
TABLE II __________________________________________________________________________ Δλ σ is PEAK σ is STABLE σ is UNSTABLE λ.sub.error Positive Zero Negative Positive Zero Negative Positive Zero Negative __________________________________________________________________________ PB ZE (1) ZE (2) ZE (3) ZE (4) PM (5) ZE (6) ZE (7) ZE (8) ZE (9) PM ZE (10) ZE (11) ZE (12) ZE (13) PM (14) ZE (15) NZ (16) NZ (17) NZ (18) PS ZE (19) ZE (20) ZE (21) ZE (22) PS (23) ZE (24) NS (25) NS (26) NS (27) ZE ZE (28) ZE (29) ZE (30) ZE (31) ZE (32) ZE (33) NM (34) NM (35) NM (36) NS ZE (37) ZE (38) ZE (39) ZE (40) ZE (41) ZE (42) NB (43) NB (44) NB (45) NM NZ (46) NZ (47) NZ (48) ZE (49) ZE (50) ZE (51) NB (52) NB (53) NB (54) NB NS (55) NS (56) NS (57) ZE (58) ZE (59) ZE (60) NB (61) NB (62) NB (63) __________________________________________________________________________
__________________________________________________________________________ APPENDIX A- MATLAB FUNCTIONS __________________________________________________________________________ function [sys,x0] = slip.sub.-- flc(t,x,u,flag) % Simulate the Fuzzy Logic Traction Control System % Inputs: % u(1) to u(6) : Wheel Slip % u(7) to u(12) : current % % States: % x(1) to x(6) : Previous Wheel Slip % x(7) to x(12) : Previous Motor Current % x(13) : Generator Current Reference % x(14) : Next Time of Execution % x(15) : norm.sub.-- slip.sub.-- delta % x(16) : norm.sub.-- current.sub.-- delta % x(17) : norm.sub.-- slip.sub.-- error % x(18) : delta.sub.-- u % x(19) = slip reference estimate % x(20) = delta.sub.-- estimate % % Outputs: % y(1) : Generator Current Reference % y(2) : norm.sub.-- slip.sub.-- delta % y(3) : norm.sub.-- current.sub.-- delta % y(4) : norm.sub.-- slip.sub.-- error % y(5) : delta.sub.-- u % y(6) = slip reference estimate % y(7) = delta.sub.-- estimate % % % Update the States. if abs(flag) == 2 % Run the Control System if 20 ms have passed. if t>=x(14) % Find the highest slip. target.sub.-- wheel = 1; target.sub.-- wheel.sub.-- slip = u(1); for i = 2:6, if u(i) > target.sub.-- wheel.sub.-- slip target.sub.-- wheel = i; target.sub.-- wheel.sub.-- slip = u(i); end end % Normalize all the inputs slip.sub.-- reference = x(19); norm.sub.-- current.sub.-- delta = max(-1,min(1,(u(target.sub.-- wheel+6)- x(target.sub.-- wheel+6))/ 10)); norm.sub.-- slip.sub.-- delta = max(-1,min(1,(u(target.sub.-- wheel)-x(tar get.sub.-- wheel))/ 0.003)); norm.sub.-- slip.sub.-- error = max(-1,min(1,(u(target.sub.-- wheel)-slip. sub.-- reference)/ slip.sub.-- reference)); stability.sub.-- measure = abs(norm.sub.-- current.sub.-- delta- norm.sub.-- slip.sub.-- delta)*sign(norm.sub.-- current.sub. -- delta*norm.sub.-- slip.sub.-- delta); stability.sub.-- measure = max(-1,min(1,stability.sub.-- measure)); % Fuzzify the normalized current delta input stability.sub.-- peak = Membership.sub.-- Value(stability.sub.-- measure,1 .0,1.0,.98,0); stability.sub.-- stable = Membership.sub.-- Value(stability.sub.-- measure,0,0,1.0,1.0); stability.sub.-- unstable = Membership.sub.-- Value(stability.sub.-- measure,-1.0,-1.0,0,0.98); % Fuzzify the normalized slip delta input slip.sub.-- delta.sub.-- pos = Membership.sub.-- Value(norm.sub.-- slip.sub.-- delta,1.0,1.0,.98,0); slip.sub.-- delta.sub.-- zero = Membership.sub.-- Value(norm.sub.-- slip.sub.-- delta,0,0,1.0,1.0); slip.sub.-- delta.sub.-- neg = Membership.sub.-- Value(norm.sub.-- slip.sub.-- delta,-1,-1.0,0,.98); % Fuzzify the slip error input slip.sub.-- error.sub.-- pos.sub.-- big = Membership.sub.-- Value(norm.sub .-- slip.sub.-- error,1.000,1.000,0.333,0.000); slip.sub.-- error.sub.-- pos.sub.-- medium = Membership.sub.-- Value(norm. sub.-- slip.sub.-- error,0.667,0.667,0.333,0.333); slip.sub.-- error.sub.-- pos.sub.-- small = Membership.sub.-- Value(norm. sub.-- slip.sub.-- error,0.333,0.333,0.333,0.333); slip.sub.-- error.sub.-- zero = Membership.sub.-- Value(norm.sub.-- slip.sub.-- error,0.000,0.000,0.333,0.333); slip.sub.-- error.sub.-- neg.sub.-- small = Membership.sub.-- Value(norm.s ub.-- slip.sub.-- error,-0.333,- 0.333,0.333,0.333); slip.sub.-- error.sub.-- neg.sub.-- medium = Membership.sub.-- Value(norm. sub.-- slip.sub.-- error,-0.667,- 0.667,0.333,0.333); slip.sub.-- error.sub.-- neg.sub.-- big = Membership.sub.-- Value(norm.sub .-- slip.sub.-- error,-1.000,- 1.000,0.000,0.333); % Zero the arrays w = zeros(7,9); y = zeros(7,9); z = zeros(7,9); % Fill the three 3D Matrixes of Fuzzy Values w(1,1:9) = ones(1,9)*slip.sub.-- error.sub.-- pos big; w(2,1:9) = ones(1,9)*slip.sub.-- error.sub.-- pos.sub.-- medium; w(3,1:9) = ones(1,9)*slip.sub.-- error.sub.-- pos.sub.-- small; w(4,1:9) = ones(1,9)*slip.sub.-- ezror.sub.-- zero; w(5,1:9) = ones(1,9)*slip.sub.-- error.sub.-- neg.sub.-- small; w(6,1:9) = ones(1,9)*slip.sub.-- error.sub.-- neg.sub.-- medium; w(7,1:9) = ones(1,9)*slip.sub.-- error.sub.-- neg.sub.-- big; y(1:7,1) = ones(7,1)*slip.sub.-- delta.sub.-- pos; y(1:7,2) = ones(7,1)*slip.sub.-- delta.sub.-- zero; y(1:7,3) = ones(7,1)*slip.sub.-- delta.sub.-- neg; y(1:7,4) = ones(7,1)*slip.sub.-- delta.sub.-- pos; y(1:7,5) = ones(7,1)*slip.sub.-- delta.sub.-- zero; y(1:7,6) = ones(7,1)*slip.sub.-- delta.sub.-- neg; y(1:7,7) = ones(7,1)*slip.sub.-- delta.sub.-- pos; y(1:7,8) = ones(7,1)*slip.sub.-- delta.sub.-- zero; y(1:7,9) = ones(7,1)*slip.sub.-- delta.sub.-- neg; z(1:7,1:3) = ones(7,3)*stability.sub.-- peak; z(1:7,4:6) = ones(7,3)*stability.sub.-- stable; z(1:7,7:9) = ones(7,3)*stability.sub.-- unstable; % AND all the variables together to get a reference state match. result = min(w,y); result = min(result,z); % Set the center of gravities for the output sets. NB = -0.800; NM = -0.600; NS = -0.400; NZ = -0.200; ZE = 0; PZ = 0.200; PS = 0.400; PM = 0.600; PB = 0.800; % Knowledge Base in tabular format. KB = [ NB,NB,NS,NM,NM,NZ,NB,NM,NM NB,NM,NZ,NM,NS,ZE,NB,NM,NM NB,NS,ZE,NM,NZ,PZ,NB,NM,NM NM,NZ,PZ,NS,ZE,PS,NB,NM,NM NS,ZE,PS,NZ,PZ,PM,NM,NM,NS NZ,PZ,PS,ZE,PS,PM,NM,NM,NS ZE,PS,PS,PZ,PM,PM,NS,NS,NS ]; % Knowledge Base in tabular format. ESTIMATOR.sub.-- KB = [ ZE,ZE,ZE,ZE,PM,ZE,ZE,ZE,ZE ZE,ZE,ZE,ZE,PM,ZE,NZ,NZ,NZ ZE,ZE,ZE,ZE,PS,ZE,NS,NS,NS ZE,ZE,ZE,ZE,ZE,ZE,NM,NM,NM ZE,ZE,ZE,ZE,ZE,ZE,NB,NB,NB NZ,NZ,NZ,ZE,ZE,ZE,NB,NB,NB NS,NS,NS,ZE,ZE,ZE,NB,NB,NB ]; % Zero the height method defuzzification counters. sum.sub.-- a = 0; sum.sub.-- b = 0; sum.sub.-- c = 0; sum.sub.-- d = 0; % Find the final output by using the height method. for i = 1:7 for j = 1:9 sum.sub.-- a = sum.sub.-- a + KB(i,j) * result(i,j); sum.sub.-- b = sum.sub.-- b + result(i,j); sum.sub.-- c = sum.sub.-- c + ESTIMATOR KB(i,j) * result(i,j); sum.sub.-- d = sum.sub.-- d + result(i,j); end end delta.sub.-- u = sum.sub.-- a/sum.sub.-- b; delta.sub.-- estimate = sum.sub.-- c/sum.sub.-- d; % Update all the states. x(1:12) = u; x(13) = x(13)+delta.sub.-- u*100; x(14) = x(14)+0.02; x(15) = norm.sub.-- slip.sub.-- delta; x(16) = norm.sub.-- current.sub.-- delta; x(17) = norm.sub.-- slip.sub.-- error; x(18) = delta.sub.-- u; x(19) = max(0.02,min(0.25,x(19)+delta.sub.-- estimate*0.01)); x(20) = delta.sub.-- estimate; tmp = [stability.sub.-- measure,norm.sub.-- current.sub.-- delta,nor m.sub.-- slip.sub.-- delta,norm.sub.-- s lip.sub.-- error,delta.sub.-- u,delta.sub.-- estimate] sys = x; else sys = x; end % Set the system outputs. elseif flag == 3 sys = [x(13),x(15),x(16),x(17),x(18),x(19),x(20)]; % Initialize the system setting and states. elseif flag == 0 sys = [0,20,7,12,0,0]; x0 = [-1*ones(1,6),zeros(1,6),8400,0,0,0,0,0,0.08,0]; % Set the Next Run Time. elstif flag == 4 sys = t + 0.020: else sys=[]; else __________________________________________________________________________
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